This project will produce a method for constructing treatment plans with a guarantee on the quality of the solution. The plans produced by current techniques can fall short of the optimum or needlessly fail to satisfy constraints. As a result, the search for an improved solution is open-ended, exhausting hospital resources and manpower, and providing no assurance to patient or physician that a better plan was not overlooked. This application proposes to use the theory of mixed integer programming to provide a solution whose objective lies within a defined range of the highest possible value obtainable under the constraints (e.g., one fraction size, 1.8 Gy). The method will accept absolute dose limits, dose volume limits and dose homogeneity limits and will be applied to both conformal therapy and intensity modulated therapy. The effect on the objective of making small changes to the constraints will be found, giving the physician and patient better control of the competing risks of treatment. It will also find the minimum number of beams needed, significantly reducing treatment cost. If successful, the method will be patented and marketed to the radiotherapy community. It will provide improved outcomes, reduce provider risks and make planning more efficient. PROPOSED COMMERCIAL APPLICATIONS: This work will develop a software algorithm that can be marketed for treatment planning. The software will reduce the costs of radiotherapy planning, improve achievable tumor doses, provide assurance that inferior plans are not created and reveal information to physicians on the tradeoffs among the risks and benefits of treatment.